MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 More Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on an exam that consists of true-false questions? 08 B) ) In how many ways can you answer the questions on an exam that consists of 8 multiple choice questions, each of which has answer choices? 65,536 B) ,376 65,306 3) In how many ways can you answer the questions on an exam that consists of 5 multiple choice questions, each of which has answer choices, followed by 7 true-false questions? 8,6 B) 3,07 7,77 55,90 ) ) 3) ) How many automobile license plates can be made involving letters followed by 3 digits? ) 696,500 B) ,7 676,000 5) How many automobile license plates can be made involving letters followed by either or 3 digits? 83,600 B) 73, ,600 73,600 6) How many 0 letter strings can be formed with the letters D, E, F, and G, if each letter can be used more than once?,08,776 B),08,576,08,536,08,656 7) The code for some garage door openers consists of electrical switches that can be set to "+", "0", or "-" by the owner. With this type of opener, how many different codes are possible?,78,769 B),78,9,78,7,78,969 8) A person ordering a certain model of car can choose any of 5 colors, either manual or automatic transmission, and any of 9 audio systems. How many ways are there to order this model of car? 98 B) ) In the "Big Bucks" lottery game, a person is to pick digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game? 6, B) 0,000 00,000,08,576 0) How many automobile license plates can be made involving 3 letters followed by digits, if letters cannot be repeated ( used more than once ) but digits can be repeated? 75,760,000 B) 56,69,00 55,97,00 56,000,000 5) 6) 7) 8) 9) 0) Tell whether permutations or combinations are being described. ) 8 digits are selected (with possible repetition) to form a code for an alarm system. ) Combinations B) Permutations

2 ) 9 students are selected to form a committee. ) 3) 3 cards are selected from a deck of 5 to form a hand for a certain card game. 3) ) musicians are selected to form a band. ) 5) pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth. 5) 6) 8 dishwashers are ranked for performance by an independent laboratory. 6) Solve the problem. 7) There are people in a club. A committee of 6 persons is to be chosen to represent the club at a conference. In how many ways can the committee be chosen?,6,60 B) 360, ) How many committees of 5 people can be selected from 5 men and 8 women if the committee must have 3 men and women? 60 B) ) 8) 9) There are 0 different books on a table. In how many ways can 6 books be chosen? 9) 0 B) 636 5,00 5,00 0) A game involves choosing 9 numbers from the numbers through 3. In how many ways can this be done? 59,59,00 B) ) There are 9 books on a reading list for English I. Students must select books to read from this list. In how many ways can the books be selected? 6 B) ) There are essay questions on a test. Students must select 3 questions to write essays on. In how many ways can the 3 questions be chosen? 8 B) ) Cal is packing his suitcase to go on a trip. He wants to pack pairs of pants chosen from the 9 pairs of pants in his closet and 3 shirts chosen from the shirts in his closet. In how many ways can this be done?,993,760 B),70 0,790 98,960 0) ) ) 3) ) How many ways are there to choose 9 books from a collection of different books? ) 55 B) ,833,600

3 Solve. 5) A baseball manager has 0 players of the same ability. How many 9 player starting lineups can he create? 90 B) 0 36,880 3,68,800 6) In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 5 at a time? 50 B) ) How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members? 36 B) ) A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown? 79 B) ) There are 6 women running in a race. How many first, second, and third place possibilities can occur? 8 B) ) A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program? 670 B) 0 3, ) 6) 7) 8) 9) 30) 3) In how many ways can 6 people line up for play tickets? 3) 6,656 B) ) How many different three-digit numbers can be written using digits from the set {,, 3,, 5} without any repeating digits? 0 B) ) How many different three-number "combinations" are possible on a combination lock having 7 numbers on its dial? 33,696 B) 7, ,88 3) 33) Expand the binomial. 3) (x + 3) 3) (6x + x + 9) B) 768x + 30 x3 + 86x + 96x x + 768x3 + 86x + 3x x x + 86x ) (-x - y) 35) 56x + 89x3y + 30xy + 8xy3 + 6y B) 56x + 89x3y - 30xy + 8xy3-6y 56x + 5x3y + 38xy + 8xy3 + 6y 56x + 5x3y - 38xy + 8xy3-6y 3

4 Find the coefficient of the given term in the binomial expansion. 36) x7y term, (x + y)9 36) 36 B) 7 8,0 5,90 37) x term, (x - ) 37),0 B) -53,0 53,0 -,0 Find the probability of the event. 38) Give the probability that the roll of a die will show or 6. 38) 3 B) 3 39) Give the probability that the roll of a die will show a number less than. 39) B) 3 3 0) Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be? B) 3 3 0) ) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 0? B) ) ) If two 8-sided dice are rolled, what is the probability that both numbers will be even? ) B) ) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 5? 3) 5 6 B) ) A coin and a six-sided die are tossed. What is the probability of getting heads and a number less than or equal to? ) 3 B) An experiment is conducted for which the sample space is S = {a, b, c, d}. Decide if the given probability function is valid. 5) 5) Outcome Probability a 5/6 b 5/8 c /8 d -/6 Yes B) No

5 Find the probability. 6) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, and 0.5 yellow. What is the probability that a randomly selected candy from a newly-opened bag will be green? B) ) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, 0. purple and 0.3 yellow. What is the probability that a randomly selected candy from a newly-opened bag will be blue or red? 0. B) ) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, 0. purple and 0. yellow. What is the probability that a randomly selected candy from a newly-opened bag will be neither red nor green? 0.6 B) ) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, 0. purple and 0.3 yellow. Suppose a candy is selected randomly from each of two newly-opened bags. What is the probability that both will be red? 0.99 B) ) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, 0. purple and 0.3 yellow. Suppose a candy is selected randomly from each of two newly-opened bags. What is the probability that neither will be red? 0.8 B) ) The maker of a certain candy claims that the proportions of colors of candy produced are: 0. red, 0. blue, 0. green, 0. purple and 0.6 yellow. Suppose a candy is selected randomly from each of two newly-opened bags. What is the probability that one is green and the other is blue? 0. B) ) A 5-card hand is dealt from a deck of 5 cards. What is the probability that a) all are from the same suit? b) all are hearts? c) exactly are spades? a) b) c) B) a) b) c) a) b) c) 0.78 a) b) c) ) A 5-card hand is dealt from a deck of 5 cards. What is the probability that a) none are queens? b) all are queens? a) b) 0 B) a) 0 b) a) 0 b) a) b) 0 6) 7) 8) 9) 50) 5) 5) 53) 5) A 7-card hand is dealt from a deck of 5 cards. What is the probability that all 7 cards are hearts? 5) B) ) A 5-card hand is dealt from a deck of 5 cards. What is the probability that 3 cards are queens and two are kings? B) ) 5

6 56) A 5-card hand is dealt from a deck of 5 cards. What is the probability that exactly one card is a king? 0.00 B) ) A 5-card hand is dealt from a deck of 5 cards. What is the probability that exactly two cards are kings? B) ) A 7-card hand is dealt from a deck of 5 cards. What is the probability that the hand includes all four kings? B) ) 57) 58) Solve the problem. 59) If P( = 0.6, P(B) = 0.5, and P(A and B) = 0.3, then what is P(A or B)? 59). B) ) If P( = 0.5, P(B) = 0., and P(A or B) = 0.7, then what is P(A and B)? 60) 0. B) ) If Elizabeth eats dinner at home tonight, there is a 0% chance that she will eat dessert. If she eats dinner at a restaurant, there is a 80% chance that she will eat dessert. Suppose that there is a 75% chance that Elizabeth will eat out tonight. What is the probability that she will eat dessert tonight? 0.6 B) ) Eleven dimes dated 989 through 999 are tossed. Find the probability of the event. 6) Heads on the 996 dime only 6) B) ) Heads on the 990 and 995 dimes only 63) B) ) Heads on all eleven dimes 6) B) ) At least one head 65) 7 B) ) Exactly heads 66) 55 B) ) Exactly heads 67) B)

7 68) Tails on all but one dime 68) 53 B)